Abstract
The influence of a one dimensional [1d] electron band over the lattice leads to the well known Peierls distortion and the enhanced Kohn anomaly [1]. Fig. la shows the occuring of a Peierls distortion for the special case of a half filled band. A distortion with a periodicity of 2c creates a gap at kF which causes the electrons to flow from occupied higher states to lower ones [Fig. 1b]. Thus the kinetic energy of the electronic system will be lowered. As the distortion will happen on the expense of elastic energy there will be an equilibrium state with a finite distortion which is the Peierls state. By a Peierls distortion we get a zone boundary at kF or a new reciprocal lattice point at 2kF and thus this effect is observable at wave vectors q = 2kF in the elastic scattering.
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References
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Renker, B., Comès, R. (1975). X-Ray and Neutron Diffraction Studies of the Peierls Instability. In: Keller, H.J. (eds) Low-Dimensional Cooperative Phenomena. NATO Advanced Study Institutes Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7031-2_12
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